Question

A milk container of height 16 cm is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.

Answer 1

Given that, height of milk container (h) = 16 cm,

Radius of lower end of milk container (r) = 8 cm

And radius of upper end of milk container (R) = 20 cm 

∴ Volume of the milk container made of metal sheet in the form of a frustum of a cone

= `(πh)/3 (R^2 + r^2 + Rr)`

= `22/7 xx 16/3 [(20)^2 + (8)^2 + 20 xx 8]`

= `(22 xx 16)/21 (400 + 64 + 160)`

= `(22 xx 16 xx 624)/21`

= `219648/21`

= 10459.42 cm³  ......[∵ 1L = 1000 cm³]

= 10.45942 L

So, volume of the milk container is 10459.42 cm³

∵ Cost of 1 L milk = ₹ 22

∴ Cost of 10.45942 L milk = 22 × 10.45942 = ₹ 230.12

Hence, the required cost of milk is ₹ 230.12